Magnetoelastic coupling in helimagnets: A molecular-field theory of the 1/4 lock-in phase of holmium

A free energy formulated within the molecular-field treatment of a Heisenberg-like Hamiltonian serves as the basis for a model of the recently reported wave-vector lock-in at Q=1/4c * in the incommensurate hexagonal helimagnet Ho. Variation of the exchange integral with interionic distance is shown to provide a mechanism for the observed decrease of Q as the temperature is lowered below TN{}131 K. Umklapp terms of the form Δ4Q,G are then responsible for stabilizing the 1/4 commensurate phase over a narrow temperature region around 96 K. A crucial ingredient of the model is a symmetry-breaking term, which distorts the polarization of the spin density from helical to elliptical. Such an interaction can arise from the basal-plane component of an applied magnetic field or of uniaxial stress. Agreement between the model and experimental results for a wide range of magnetic properties is demonstrated using numerical estimates for a relatively small number of exchange parameters.